What Converges in the Platonic Representation Hypothesis? Structure over Geometry

arXiv:2609.27252 · cs.LG, cs.CV, math.AT · Submitted 2026-09-23 · Read on arXiv

cs.LG, cs.CV, math.AT

Submitted: 2026-09-23

Updated: 2026-09-23

Comments: 33 pages, 12 figures, 6 tables

Code: https://github.com/junwon0/what-converges-prh

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Alignment — 218× in this paper · explained in 1 episode
• Aggregation — 39× in this paper · explained in 1 episode
• Calibration — 26× in this paper · explained in 7 episodes
• Platonic Representation Hypothesis — 7× in this paper
• Alignment Scores — 6× in this paper · explained in 1 episode
• Transformer — 6× in this paper · explained in 2 episodes
• Robustness — 5× in this paper · explained in 5 episodes
• Cosine Similarity — 4× in this paper · explained in 3 episodes
• Persistent Homology — 4× in this paper · explained in 3 episodes
• Generalization — 3× in this paper · explained in 13 episodes
• Representation Learning — 3× in this paper · explained in 2 episodes
• Consistency — 2× in this paper · explained in 3 episodes
• Regularization — 2× in this paper · explained in 3 episodes
• Adam — 1× in this paper · explained in 2 episodes
• Alignment Methods — 1× in this paper · explained in 1 episode
• Benchmark — 1× in this paper · explained in 2 episodes
• Distillation — 1× in this paper · explained in 2 episodes
• Embeddings — 1× in this paper · explained in 2 episodes
• Fine-Tuning — 1× in this paper · explained in 5 episodes
• Grounding — 1× in this paper · explained in 3 episodes
• Interpretability — 1× in this paper · explained in 15 episodes
• Knowledge Distillation — 1× in this paper · explained in 11 episodes
• Representational Similarity Analysis — 1× in this paper
• Scaling Laws — 1× in this paper · explained in 4 episodes

Sources

• Representation Topology Divergence: A Method for Comparing Neural Network Representations
• Convergent Learning: Do different neural networks learn the same representations?
• Gemma 2: Improving Open Language Models at a Practical Size
• LLaMA: Open and Efficient Foundation Language Models
• Topology-Aware Representation Alignment for Semi-Supervised Vision-Language Learning

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